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Administrative Studies

ADMS 2320

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CHAPTER 11 SECTION 2: INTRODUCTION TO HYPOTHESIS TESTING
MULTIPLE CHOICE
56. In testing the hypotheses 0 : μ = 50 vs.1H : μ ≠ 50, the following information is known: n = 64, =
53.5, and σ = 10. The standardized test statistic z equals:
a. 1.96
b. −2.80
c. 2.80
d. −1.96
ANS: C PTS: 1 REF: SECTION 11.2
57. If a hypothesis is not rejected at the 0.10 level of significance, it:
a. must be rejected at the 0.05 level.
b. may be rejected at the 0.05 level.
c. will not be rejected at the 0.05 level.
d. must be rejected at the 0.025 level.
ANS: C PTS: 1 REF: SECTION 11.2
58. In order to determine the p-value, which of the following is not needed?
a. The level of significance.
b. Whether the test is one-tail or two-tail.
c. The value of the test statistic.
d. All of these choices are true.
ANS: A PTS: 1 REF: SECTION 11.2
59. In testing the hypotheses 0 : μ = 75 vs.1H : μ < 75, if the value of the test statistic z equals −2.42, then
the p-value is:
a. 0.5078
b. 2.4200
c. 0.9922
d. 0.0078
ANS: D PTS: 1 REF: SECTION 11.2
60. For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of
the standardized test statistic z is:
a. smaller than 1.96 or greater than −1.96
b. greater than −1.96 or smaller than 1.96
c. smaller than −1.96 or greater than 1.96
d. greater than 1.645 or less than −1.645
ANS: C PTS: 1 REF: SECTION 11.2
This edition is intended copied, or distributed without the prior consent of the publisher.nt from the U.S. Edition. This may not be resold, 61. In testing the hypotheses 0 : μ = 800 vs1 H : μ ≠ 800, if the value of the test statistic equals 1.75, then
the p-value is:
a. 0.0401
b. 0.0802
c. 0.4599
d. 0.9599
ANS: B PTS: 1 REF: SECTION 11.2
62. If a hypothesis is rejected at the 0.025 level of significance, it:
a. must be rejected at any level.
b. must be rejected at the 0.01 level.
c. must not be rejected at the 0.01 level.
d. may or may not be rejected at the 0.01 level.
ANS: D PTS: 1 REF: SECTION 11.2
63. Which of the following p-values will lead us to reject the null hypothesis if the level of significance
equals 0.05?
a. 0.150
b. 0.100
c. 0.051
d. 0.025
ANS: D PTS: 1 REF: SECTION 11.2
64. Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the
following α-values do we also reject the null hypothesis?
a. 0.06
b. 0.04
c. 0.03
d. 0.02
ANS: A PTS: 1 REF: SECTION 11.2
65. The critical valuesαz orαz/ 2e the boundary values for:
a. the rejection region(s).
b. the level of significance.
c. Type I error.
d. Type II error.
ANS: A PTS: 1 REF: SECTION 11.2
66. In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative
hypothesis is true:
a. a Type I error is committed.
b. a Type II error is committed.
c. a correct decision is made.
d. a one-tail test should be used instead of a two-tail test.
ANS: C PTS: 1 REF: SECTION 11.2
This edition is intended copied, or distributed without the prior consent of the publisher.nt from the U.S. Edition. This may not be resold, 67. Using a confidence interval when conducting a two-tail test for μ, we do not reject H0if the
hypothesized value for μ:
a. is to the left of the lower confidence limit (LCL).
b. is to the right of the upper confidence limit (UCL).
c. falls between the LCL and UCL.
d. falls in the rejection region.
ANS: C PTS: 1 REF: SECTION 11.2
68. In a two-tail test for the population mean, the null hypothesis will be rejected at α level of significance
if the value of the standardized test statistic z is such that:
a. z > z α
b. z < −zα
c. −zα< z < zα
d. | z | > α/ 2
ANS: D PTS: 1 REF: SECTION 11.2
69. In testing the hypothesis H0: μ = 100 vs. H1: μ > 100, the p-value is found to be 0.074, and the sample
mean is 105. Which of the following statements is true?
a. The probability of observing a sample mean at least as large as 105 from a population
whose mean is 100 is 0.074.
b. The probability of observing a sample mean smaller than 105 from a population whose
mean is 100 is 0.074.
c. The probability that the population mean is larger than 100 is 0.074.
d. None of these choices.
ANS: A PTS: 1 REF: SECTION 11.2
70. If we reject the null hypothesis, we conclude that:
a. there is enough statistical evidence to infer that the alternative hypothesis is true.
b. there is not enough statistical evidence to infer that the alternative hypothesis is true.
c. there is enough statistical evidence to infer that the null hypothesis is true.
d. there is not enough statistical evidence to infer that the null hypothesis is true.
ANS: A PTS: 1 REF: SECTION 11.2
71. Suppose that in a certain hypothesis test the null hypothesis is rejected at the .10 level; it is also
rejected at the .05 level; however it cannot be rejected at the .01 level. The most accurate statement
that can be made about the p-value for this test is that:
a. p-value = 0.01.
b. p-value = 0.10.
c. 0.01 < p-value < 0.05.
d. 0.05 < p-value < 0.10.
ANS: C PTS: 1 REF: SECTION 11.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher. 72. Statisticians can translate p-values into several descriptive terms. Suppose you typically reject0H at
level 0.05. Which of the following statements is correct?
a. If the p-value < 0.001, there is overwhelming evidence to infer that the alternative
hypothesis is true.
b. If 0.01 < p-value < 0.05, there is evidence to infer that the alternative hypothesis is true.
c. If p-value > 0.10, there is no evidence to infer that the alternative hypothesis is true.
d. All of these choices are true.
ANS: D PTS: 1 REF: SECTION 11.2
73. If we do not reject the null hypothesis, we conclude that:
a. there is enough statistical evidence to infer that the alternative hypothesis is true.
b. there is not enough statistical evidence to infer that the alternative hypothesis is true.
c. there is enough statistical evidence to infer that the null hypothesis is true.
d. there is not enough statistical evidence to infer that the null hypothesis is true.
ANS: B PTS: 1 REF: SECTION 11.2
74. In a one-tail test, the p-value is found to be equal to 0.068. If the test had been two-tail, the p-value
would have been:
a. 0.932
b. 0.466
c. 0.034
d. 0.136
ANS: D PTS: 1 REF: SECTION 11.2
75. If the value of the sample mean is close enough to the hypothesized value μ of the population mean
0
μ, then:
a. the value of μ0is definitely correct.
b. the value of μ0is definitely wrong.
c. we reject the null hypothesis.
d. we cannot reject the null hypothesis.
ANS: D PTS: 1 REF: SECTION 11.2
76. The p-value of a test is the:
a. smallest α at which the null hypothesis can be rejected.
b.
largest α at which the null hypothesis can be rejected.
c. smallest α at which the null hypothesis cannot be rejected.
d. largest α at which the null hypothesis cannot be rejected.
ANS: A PTS: 1 REF: SECTION 11.2
77. We have created a 95% confidence interval for μ with the result (8, 13). What conclusion will we
make if we test H : μ = 15 vs. H : μ ≠ 15 at α = 0.05?
0 1
a. Reject H i0 favor of H 1
b. Accept H in0favor of H 1
c. Fail to reject H0in favor of H1
d. We cannot tell what our decision will be from the information given
ANS: A PTS: 1 REF: SECTION 11.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher. 78. The p-value criterion for hypothesis testing is to reject the null hypothesis if:
a. p-value = α
b. p-value < α
c. p-value > α
d. −α < p-value < α
ANS: B PTS: 1 REF: SECTION 11.2
79. If the p value is less than α in a two-tail test:
a. the null hypothesis should not be rejected.
b. the null hypothesis should be rejected.
c. a one-tail test should be used.
d. No conclusion should be reached.
ANS: B PTS: 1 REF: SECTION 11.2
80. If an economist wishes to determine whether there is evidence that average family income in a
community exceeds $32,000:
a. either a one-tail or two-tail test could be used with equivalent results.
b. a one-tail test should be utilized.
c. a two-tail test should be utilized.
d. None of these choices.
ANS: B PTS: 1 REF: SECTION 11.2
81. We have created a 95% confidence interval for μ with the results (10, 25). What conclusion will we
make if we test H : μ = 26 vs. H : μ ≠ 26 at α = 0.025?
0 1
a. Reject H i0 favor of H 1
b. Accept H i0 favor of H 1
c. Fail to reject H0in favor of H1
d. We cannot tell from the information given.
ANS: D PTS: 1 REF: SECTION 11.2
82. The rejection region for testing H0: μ = 100 vs. H1: μ ≠ 100, at the 0.05 level of significance is:
a. | z | < 0.95
b. | z | > 1.96
c. z > 1.65
d. z < 2.33
ANS: B PTS: 1 REF: SECTION 11.2
83. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the
club. She would now like to determine whether or not the mean age of her customers is over 35. If so,
she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will
be made. Suppose she found that the sample mean was 35.5 years and the population standard
deviation was 5 years. What is the p-value associated with the test statistic?
a. 0.9582
b. 1.7300
c. 0.0418
d. 0.0836
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher. ANS: C PTS: 1 REF: SECTION 11.2
84. It is possible to directly compare the results of a confidence interval estimate to the results obtained by
testing a null hypothesis if:
a. a two-tail test for μ is used.
b.
a one-tail test for μ is used.
c. a two-tail test for is used.
d. a one-tail test for is used.
ANS: A PTS: 1 REF: SECTION 11.2
85. The rejection region for testing H0: μ = 80 vs. 1 : μ < 80, at the 0.10 level of significance is:
a. z > 1.96
b. z < 0.90
c. z > 1.28
d. z < −1.28
ANS: D PTS: 1 REF: SECTION 11.2
86. We have created a 90% confidence interval for μ with the result (25, 32). What conclusion will we
make if we test H0: μ = 28 vs. H1: μ ≠ 28 at α = 0.10?
a. Reject H i0 favor of H .1
b. Accept H i0 favor of H . 1
c. Fail to reject H in favor of H .
0 1
d. We cannot tell from the information given.
ANS: C PTS: 1 REF: SECTION 11.2
87. The numerical quantity computed from the data that is used in deciding whether to reject H 0s the:
a. significance level.
b. critical value.
c. test statistic.
d. parameter.
ANS: C PTS: 1 REF: SECTION 11.2
88. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the
club. She would now like to determine whether or not the mean age of her customers is over 35. If so,
she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will
be made. If she wants to be 99% confident in her decision, what rejection region she use if the
population standard deviation σ is known?
a. Reject H i0 z < −2.33
b. Reject H 0f z < −2.58
c. Reject H i0 z > 2.33
d. Reject H i0 z > 2.58
ANS: C PTS: 1 REF: SECTION 11.2
TRUE/FALSE
89. A one-tail p-value is two times the size of a two-tail test.
ANS: F PTS: 1 REF: SECTION 11.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher. 90. A p-value is usually set at 0.05.
ANS: F PTS: 1 REF: SECTION 11.2
91. The p-value of a test is the probability of observing a test statistic at least as extreme as the one
computed given that the null hypothesis is true.
ANS: T PTS: 1 REF: SECTION 11.2
92. For a given level of significance, if the sample size is increased, the probability of committing a Type
II error will decrease.
ANS: T PTS: 1 REF: SECTION 11.2
93. The critical values will bound the rejection and non-rejection regions for the null hypothesis.
ANS: T PTS: 1 REF: SECTION 11.2
94. If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer
that the null hypothesis is true.
ANS: F PTS: 1 REF: SECTION 11.2
95. The p-value of a test is the smallest α at which the null hypothesis can be rejected.
ANS: T PTS: 1 REF: SECTION 11.2
96. If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level.
ANS: F PTS: 1 REF: SECTION 11.2
97. In a one-tail test, the p-value is found to be equal to 0.054. If the test had been two-tail, then the p-
value would have been 0.027.
ANS: F PTS: 1 REF: SECTION 11.2
98. A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence
interval goes from 78.21 to 87.64. If the same sample had been used to test the null hypothesis that the
mean of the population differs from 90, the null hypothesis could be rejected at a level of significance
of 0.05.
ANS: T PTS: 1 REF: SECTION 11.2
99. The p-value is the probability that the null hypothesis is true.
ANS: F PTS: 1 REF: SECTION 11.2
100. In order to determine the p-value, it is necessary to know the level of significance.
ANS: F PTS: 1 REF: SECTION 11.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher. 101. If we reject a null hypothesis at the 0.05 level of significance, then we must also reject it at the 0.10
level.
ANS: T PTS: 1 REF: SECTION 11.2
102. If your p-value is greater than 0.900 you should r0ject H at the 0.10 level.
ANS: F PTS: 1 REF: SECTION 11.2
103. A p-value is a probability, and must be between 0 and 1.
ANS: T PTS: 1 REF: SECTION 11.2
104. A one-tail test for the population mean μ produces a test-statistic z = −0.75. The p-value associated
with the test is 0.7734.
ANS: F PTS: 1 REF: SECTION 11.2
105. Using the confidence interval when conducting a two-tail test for the population mean μ, we do not

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